Editing Mechanism design (section)

===Gibbard–Satterthwaite theorem===

{{main|Gibbard–Satterthwaite theorem}}

{{harvs|txt|last=Gibbard|year=1973|author-link=Allan Gibbard}} and {{harvs|txt|last=Satterthwaite|year=1975|author-link=Mark Satterthwaite}} give an impossibility result similar in spirit to [[Arrow's impossibility theorem]]. For a very general class of games, only "dictatorial" social choice functions can be implemented.

A social choice function <math>f(\cdot)</math> is '''dictatorial''' if one agent always receives his most-favored goods allocation,
:<math>\text{for } f(\Theta)\text{, } \exists i \in I \text{ such that } u_i(x,\theta_i) \geq u_i(x',\theta_i) \ \forall x' \in X</math>

The theorem states that under general conditions any truthfully implementable social choice function must be dictatorial if,
# ''X'' is finite and contains at least three elements
# Preferences are rational
# <math>f(\Theta) = X</math>